- Find the phase relationship between this wavefoe v= 50 sin (uwt - 20) i = 10 sin (wt +50)
- Find the phase relationship between this wavefoe v= 50 sin (uwt - 20) i = 10 sin (wt +50)
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Author:Robert L. Boylestad
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![**Phase Relationship Calculation Between Waveforms**
Given the following waveforms:
\[ v = 50 \sin (\omega t - 20^\circ) \]
\[ i = 10 \sin (\omega t + 50^\circ) \]
We are to determine the phase relationship between these two waveforms.
**Steps to Determine Phase Relationship:**
1. Identify the phase angles of each waveform.
- For the voltage \( v \):
\[ \text{Phase angle} = -20^\circ \]
- For the current \( i \):
\[ \text{Phase angle} = +50^\circ \]
2. Calculate the phase difference between the two waveforms.
- Let \( \phi_v \) be the phase angle for voltage and \( \phi_i \) be the phase angle for current.
\[ \phi_v = -20^\circ \]
\[ \phi_i = +50^\circ \]
The phase difference \( \Delta \phi \) is given by:
\[ \Delta \phi = \phi_i - \phi_v \]
\[ \Delta \phi = 50^\circ - (-20^\circ) \]
\[ \Delta \phi = 50^\circ + 20^\circ \]
\[ \Delta \phi = 70^\circ \]
Therefore, the phase relationship between the voltage and the current is a phase difference of 70 degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2405e5cb-20d1-4277-a72a-e2ca429d5d5b%2Fa9bb9182-fc87-45e7-9ecd-c9fe5d88999b%2F9tui6u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Phase Relationship Calculation Between Waveforms**
Given the following waveforms:
\[ v = 50 \sin (\omega t - 20^\circ) \]
\[ i = 10 \sin (\omega t + 50^\circ) \]
We are to determine the phase relationship between these two waveforms.
**Steps to Determine Phase Relationship:**
1. Identify the phase angles of each waveform.
- For the voltage \( v \):
\[ \text{Phase angle} = -20^\circ \]
- For the current \( i \):
\[ \text{Phase angle} = +50^\circ \]
2. Calculate the phase difference between the two waveforms.
- Let \( \phi_v \) be the phase angle for voltage and \( \phi_i \) be the phase angle for current.
\[ \phi_v = -20^\circ \]
\[ \phi_i = +50^\circ \]
The phase difference \( \Delta \phi \) is given by:
\[ \Delta \phi = \phi_i - \phi_v \]
\[ \Delta \phi = 50^\circ - (-20^\circ) \]
\[ \Delta \phi = 50^\circ + 20^\circ \]
\[ \Delta \phi = 70^\circ \]
Therefore, the phase relationship between the voltage and the current is a phase difference of 70 degrees.
![### Problem Statement for Educational Website:
10. For the following waveform, find:
#### a) Write the equation representation for the waveform when "wt" is:
- 90°: __________
- 170°: __________
- -10°: __________
#### b) Find the instantaneous value (at):
- a) 90°: __________
- b) 170°: __________
- c) -10°: __________
### Description of the Graph:
The graph represents a sinusoidal waveform (sine wave) plotted on a Cartesian plane, with the vertical axis labeled as "V" (voltage) and the horizontal axis labeled as "wt" (angular displacement in degrees).
Key Points on the Graph:
- The waveform has a peak value (amplitude) of 10 V.
- The waveform crosses the voltage axis at 0°, 80°, 170°, and 350°.
- The graph extends from an amplitude of 10 V to -10 V.
- The waveform completes one full cycle from 0° to 350°.
### Note for Students:
To solve part (a) and part (b) of this problem, you need to:
1. Derive the mathematical equation of the sine wave based on its amplitude and frequency.
2. Use the equation to calculate the instantaneous voltage values at the specified angular displacements (wt).
This exercise will help you understand how to represent and analyze sinusoidal waveforms in electrical engineering.
Remember, the general form of a sinusoidal waveform is:
\[ V(t) = V_m \sin(\omega t + \phi) \]
where:
- \( V_m \) is the maximum amplitude.
- \( \omega t \) is the angular frequency multiplied by time.
- \( \phi \) is the phase shift.
Use the graph to identify these parameters!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2405e5cb-20d1-4277-a72a-e2ca429d5d5b%2Fa9bb9182-fc87-45e7-9ecd-c9fe5d88999b%2F5ifilit9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement for Educational Website:
10. For the following waveform, find:
#### a) Write the equation representation for the waveform when "wt" is:
- 90°: __________
- 170°: __________
- -10°: __________
#### b) Find the instantaneous value (at):
- a) 90°: __________
- b) 170°: __________
- c) -10°: __________
### Description of the Graph:
The graph represents a sinusoidal waveform (sine wave) plotted on a Cartesian plane, with the vertical axis labeled as "V" (voltage) and the horizontal axis labeled as "wt" (angular displacement in degrees).
Key Points on the Graph:
- The waveform has a peak value (amplitude) of 10 V.
- The waveform crosses the voltage axis at 0°, 80°, 170°, and 350°.
- The graph extends from an amplitude of 10 V to -10 V.
- The waveform completes one full cycle from 0° to 350°.
### Note for Students:
To solve part (a) and part (b) of this problem, you need to:
1. Derive the mathematical equation of the sine wave based on its amplitude and frequency.
2. Use the equation to calculate the instantaneous voltage values at the specified angular displacements (wt).
This exercise will help you understand how to represent and analyze sinusoidal waveforms in electrical engineering.
Remember, the general form of a sinusoidal waveform is:
\[ V(t) = V_m \sin(\omega t + \phi) \]
where:
- \( V_m \) is the maximum amplitude.
- \( \omega t \) is the angular frequency multiplied by time.
- \( \phi \) is the phase shift.
Use the graph to identify these parameters!
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